You can see more info about Slieveneena at this link: https://www.townlands.ie/galway/moycullen/moycullen/sliabh-an-aonaigh/s…
You can move around on the map which you'll see there to see where the townland is situated with reference to Spiddal and Galway city (which is off to the southeast). There is also access there to the census records which Roger mentioned, as well as the records for the townland in Griffith's Valuation (mid-1800's). A Mary Keady is shown in Griffith's Valuation as holding a tenancy there, but Bartly is not listed. That Mary may, however, have been Bartly's mother, if his father had died and he was too young to hold the tenancy (this is just a guess).
Here's a direct link to the list of tenants:
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=doNam…
The Catholic parish records for Moycullen which are available online go back to the 1780's (with some gaps), so you may be able to confirm the relationship if you find a baptismal record for Bartly and also find other family info there. Those records are available at this link:
https://registers.nli.ie/parishes/0633
Interestingly, the parish also appears to have extensive death records, which is not all that common.
In case you're interested, Barty was a nickname used for the given name Bartholomew, which was also sometimes recorded as Bartle, Batt, or Batty. The family would have been Irish speaking (much of the area around Spiddal still is), so the family may have used the original Irish forms of their names, although by the mid- to late-1800's anglicized forms were widely used In earlier times, the Irish given name Parthalán (which could be spelled several different ways) was in use as the name of the apostle Bartholomew, but when names came to be anglicized, it generally became Bartholomew. Sometimes the Irish name Brian was also anglicized as Bartholomew.
According to MacLysaght's Surnames of Ireland, the surname Keady comes from the Irish surname Mac Céadaigh (based on the given name Céadach). It originated in what is now County Laois, but generally disappeared from there and is now found mainly in Galway (perhaps the Keady's moved there in Cromwellian times). He says that there was another surname, Ó Meicéidigh, which was corrupted into Mac Céidigh and also became anglicized as Keady, but that was in County Cork.
He says that the surname Thornton, which is of English origin, was used as the anglicized form of several Irish surnames. One of them which is found widely in Galway is Ó Draighneán (from the word draighneán, meaning "blackthorn"), which was also sometimes anglicized as Tarrant or Drennan.
